Finite groups with \(2\)-nilpotent subgroups of even index (Q1274087)
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scientific article; zbMATH DE number 1238046
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Finite groups with \(2\)-nilpotent subgroups of even index |
scientific article; zbMATH DE number 1238046 |
Statements
Finite groups with \(2\)-nilpotent subgroups of even index (English)
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13 December 1999
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Let \(G\) be a finite group such that every subgroup of even index whose order is divisible by at most two distinct primes has a normal 2-complement. The author gives the exact structure of \(G/O(G)\). In particular, he proves that every non-abelian composition factor of \(G\) is isomorphic either to \(L_2(q\)), \(q=8r\pm 3\), or to \(L_2(2^p)\), \(p\) a prime.
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biprimary subgroups
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Shmidt groups
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Frobenius groups
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finite groups
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normal complements
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composition factors
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